Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

sorption change associated with a specific transition (tx i ) can be presentedas follows:Da i ðtxÞa 0;i ðtxÞ ¼ ne i þ n h ið3Þwhere a 0,i is the contribution of transition tx i to the ground-state absorptionspectrum.As was discussed in Section II.A, the band-edge optical properties ofNQDs are dominated by two transitions that couple the lowest 1S electronstate to two manifolds of closely spaced hole states. These transitions aremanifested in optical spectra as the 1S absorption (the ‘‘absorbing’’ transition)and the band-edge PL (the ‘‘emitting’’ transition) peaks (Fig. 1a and 1b).At moderate excitation levels for which the hole manifold of ‘‘absorbing’’states is unoccupied, the pump-induced absorption change within the ‘‘absorbing’’1S transition (tx 1S ) is solely due to the 1S electron state occupationnumber:Da 1S ðtxÞa 0 ðtxÞ¼ n e 1Sð4ÞIn order to use this expression for a comparison with an experiment, we need toeaverage n 1S over different NQD populations existing in the NQD ensemble.We perform averaging assuming a Poisson distribution of NQD populations:P(N) = hNi N e hN i /N!, where P(N ) is the probability of having N e–h pairs in aselected NQD when the average population of NQDs is hNi. The Poissondistribution is applicable if the probability of generating the e–h pair in anNQD is independent of the number of e–h pairs already existing in it. Thisassumption is valid, for example, in the case of very low excitation intensities,hNi